Abstract
In this chapter, analytical galloping dynamics of linear cables is discussed through a two-degree-of-freedom nonlinear oscillator. The nonlinearity in the two degree-of-freedom oscillator is only from aero-dynamical forces caused by the uniform airflow. The analytical solutions of periodic motions for linear cable galloping are discussed from the analytical solutions with the finite Fourier series. The corresponding stability and bifurcation analyses of the periodic motions in the galloping system of linear cable are carried out. Numerical illustrations of trajectories and amplitude spectrums are given for galloping motions in linear cables. From such analytical solutions, galloping phenomenon in flow-induced vibration can be further understood. The galloping dynamics of linear cables is similar to the dynamics of van der Pol oscillator.
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References
Luo, A. C. J. (2012). Continuous dynamical systems. Beijing/Glen Carbon: HigherEducation Press/L&H Scientific.
Luo, A. C. J. (2014). Toward analytical chaos in nonlinear systems. New York: Wiley.
Yu, B., & Luo, A. C. J. (2016). Analytical solutions of periodic motions and limit cycle in linear cable galloping. International Journal of Dynamics and Control. (in press).
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© 2017 Springer Nature Singapore Pte Ltd. and Higher Education Press, Beijing
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Luo, A.C.J., Yu, B. (2017). Linear Cable Galloping. In: Galloping Instability to Chaos of Cables. Nonlinear Physical Science. Springer, Singapore. https://doi.org/10.1007/978-981-10-5242-2_6
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DOI: https://doi.org/10.1007/978-981-10-5242-2_6
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Online ISBN: 978-981-10-5242-2
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